Combining Traditional Map Labeling with Boundary Labeling

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The traditional map labeling problems are mostly \({\mathcal{NP}}\)-hard. Hence, effective heuristics and approximations have been developed in the past. Recently, efficient algorithms for the so-called boundary labeling model have been introduced which assumes that the labels are placed on the boundary of the map and connected by polygonal leaders to their corresponding sites. Internal labels have been forbidden. In this paper, we allow both. Since clearly internal labels should be preferred, we consider several maximization problems for the number of internal labels and we show that they can be obtained efficiently or in quasi-polynomial time.